Wenliang Zhang

Email: wlzhang at uic.edu

Address: UIC MSCS Department (M/C 249)

851 S. Morgan St.

Chicago, IL 60607-7045

Papers (published or accepted):

31. Stabilization of cohomology of thickenings (with B. Bhatt, M. Blickle, G. Lyubeznik, and A. Singh)

arXiv:1605.09492, American Journal of Mathematics, accepted.

30. F-singularities under generic linkage (with L. Ma, J. Page, R. Rebhuhn-Glanz, and W. Taylor)

arXiv:1607.03972, Journal of Algebra, accepted.

29. F-singularities in families (with Z. Patakfalvi, and K. Schwede)

arXiv:1305.1646, Algebraic Geometry, accepted.

28. Global parameter test ideals (with M. Katzman, S. Murru, and J. Velez)

arXiv:1607.01947, Journal of Algebra, accepted.

27. The support of local cohomology modules (with M. Katzman)

arXiv:1509:01519, International Math. Research Notices, accepted.

26. D-module length of local cohomology modules (with M. Katzman, L. Ma, and I. Smirnov)

arXiv: 1609.01643, Trans. Amer. Math. Soc., accepted.

25. Content of local cohomology, parameter ideals, and robust algebras (with M. Hochster)

arXiv: 1609.07017, Trans. Amer. Math. Soc., accepted.

24. On injective dimension of F-finite F-modules and holonomic D-modules

arXiv:1606.00536, Bulletin of. Lond. Math. Soc., accepted.

23. Poincare duality in modular coinvariant rings (with M. Sezer)

Proc. Amer. Math. Soc., 144 (2016), no. 12, 5113–5120.

22. F-pure thresholds of homogeneous polynomials (with D. Hernandez, L. Nunez Betancourt, and E. Witt)

Michigan Math. Journal, 65 (2016), no.1, 57–87 .

21. Frobenius splitting in commutative algebra (with K. Smith)

Commutative algebra and noncommutative algebraic geometry. Vol. I, 291-345, Math. Sci. Res. Inst. Publ., 67, Cambridge Univ. Press.

20. A survey on Lyubeznik numbers (with L. Nunez Betancourt and E. Witt)

Contemp. Math. 657, 137--163.

19. An extension of a theorem of Hartshorne (with M. Katzman and G. Lyubeznik)

Proc. Amer. Math. Soc. 144 (2016), no. 3, 955--962.

18. Eulerian Graded D-modules (with L. Ma)

Math. Res. Lett. 21 (2014), no. 1, 149--167.

17. Local cohomology modules of a smooth Z-algebra have finitely many associated primes (with B. Bhatt, M. Blickle, G. Lyubeznik, and A. Singh)

Invent. Math. 197 (2014), no. 3, 509--519.

16. Rings of Frobenius operators (with M. Katzman, K. Schwede, and A. Singh)

Math. Proc. Cambridge Philos. Soc. 157 (2014), no. 1, 151–167.

15. Annihilators of Artinian modules compatible with a Frobenius map (with M. Katzman)

J. Symbolic Comput. 60 (2014), 29--46.

14. Castelnuovo-Mumford regularity and the discreteness of F-jumping coefficients in graded rings (with M. Katzman)

Trans. Amer. Math. Soc. 366 (2014), no. 7, 3519--3533.

13. Cartier modules on toric varieties (with J.-C. Hsiao, and K. Schwede)

Trans. Amer. Math. Soc. 366 (2014), no. 4, 177--1795.

12. Bertini theorems for F-singularities (with K. Schwede)

Proc. London Math. Soc., (3) 107 (2013), no. 4, 851--874.

11. Estimates for F-jumping numbers and bounds for Hartshorne-Speiser-Lyubeznik numbers (with M. Mustata)

Nagoya Math. J. 210 (2013), 133--160.

10. Test ideals via a single alteration and discreteness and rationality of F-jumping numbers (with K. Schwede and K. Tucker)

Math. Res. Letters, 19 (2012), no. 1, 191--197.

9. Two interesting examples of D-modules in characteristic p > 0 (with M. Katzman and G. Lyubeznik)

Bulletin of London Math. Soc., (2012) 44(6): 1116--1122

8. A property of the Frobenius map on a polynomial ring (with G. Lyubeznik and Y. Zhang)

Contemp. Math. 555 (Proceedings of PASI 2009), 137--144.

7. An upper bound on the number of F-jumping coefficients of a principal ideal (with M. Katzman and G. Lyubeznik)

Proc. Amer. Math. Soc. 139 (2011), 4193--4197.

6. Lyubeznik numbers of projective schemes

Adv. Math. 228 (2011), 575--616.

5. Discreteness and rationality of F-jumping numbers on singular varieties (with M. Blickle, K. Schwede, and S. Takagi)

Math. Ann. 347 (2010), no. 4, 917--949.

4. On Frobenius powers and colon ideals,

Comm. Alg. 37 (2009), no.7, 2391--2395.

3. On the localization theorem for F-pure rings (with K. Shimomoto)

Journal of Pure and Applied Algebra, (2009), no. 6, 1133--1139.

2. On the discreteness and rationality of F-jumping coefficients (with M. Katzman and G. Lyubeznik)

Journal of Algebra, 322 (2009), no. 9, 3238--3247.

1. On the highest Lyubeznik number of a local ring

Compositio Mathematica, 143 (2007), no. 1, 82--88.

Preprints (submitted or in preparation):

1. A note on growth of regularity with respect to Frobenius

arXiv:1512:00049, submitted.

2. Duality and de Rham cohomology for graded D-modules (with N. Switala)

arXiv:1705.00788, submitted.

3. A dichotomy for the injective dimension of F-finite F-modules and holonomic D-modules (with N. Switala)

arXiv:1708.06481, submitted.

4. Vanishing of local cohomology modules in mixed characteristic

in preparation.

Teaching:

Fall 2017: Math 310 (Applied Linear Algebra)

Spring 2017: Math 180 (Calculus I)

Spring 2017: Math 517 (Graduate Algebra II)

Spring 2016: Math 310 (Linear Algebra)

Fall 2015: Math 330 (Abstract Algebra)

REU: Chris Skalit, Kevin Tucker and myself are organizing an REU program in Commutative Algebra in Summer 2016. More information can be found here.

Lecture notes:

1. Local cohomology workshop at UIC, 02/27--03/01, 2015. (Notes)

2. Introduction to modular curves and modular forms, Fall 2014. (Notes)

Past Events Organized:

- D-Modules in Commutative Algebra, (08/10--08/14, 2015), CIMAT, Guanajuato, Mexico.
- Mathematical Research Community in Commutative algebra, (06/07--06/13, 2015), Snowbird, UT.
- Local cohomology workshop, (02/27--03/01, 2015), Chicago, IL.
- Focus period on Local cohomology and Regularity, (04/01--04/26, 2013), Special Year in Commutative Algebra at MSRI.
- Computational workshop on Frobenius singularities and invariants, (05/29--06/01, 2012), Ann Arbor, MI.